The new account would not only stop overdrafts from happening at the point of sale, but it would also prevent them from occurring on any other transactions, including ATM withdrawals, automatic bill payments and checks. Currently, customers are dinged with a fee of $35 each time they overdraw their accounts in these ways.

Bank of America(BAC) declined to comment on any specifics. The Wall Street Journal first reported the news, but a source familiar with the bank emphasized that the account is just a consideration at this point and does not mean the bank is getting rid of overdraft protection altogether -- it would simply be another option for customers.